Sunday, July 28, 2013

Geometric Landscape

I got shifted from my usual (of late) secondary student teacher supervision to elementary preservice teacher prep this fall. (We have an unusually low number of student teachers this fall.) I love this teaching, too, so it will be a treat. Pam Wells, David Coffey and Jon Hasenbank were already coplanning a revision to the course, so it gave me a chance to dive in and collaborate. And gave me my first chance to look in detail at the K-5 Geometry common core. So I thought I'd share what I saw:

First I collated them, then tried to look for a way to organize them more sensibly. They are pretty unevenly written. From vague generalities to hyper-specifics. The best common threads I saw were the action verbs about what the students were supposed to be able to do.

Our assignment was to sort them into a concept map or landscape of learning.  I'm very fond of the landscape of learning model for teachers. I first saw the idea in Fosnot and Dolk.  In addition to those Young Mathematicians at Work books, they are involved in the great Mathematics in the City project and the excellent curriculum Contexts for Learning Mathematics. Here's a sample chapter from the YMAW: Algebra book. This sample chapter from Contexts for Learning has a Multiplication Landscape of Learning (page 16).

A landscape emphasizes the many paths through understanding that students might take, and are loosely organized from bottom to top in terms of students development. (Read also Christopher Danielson on landscapes. Here's a landscape from years ago I developed with novice teachers for teaching money.)

Here's what I came up with. I'd love feedback on ordering from top to bottom, what you would add, and classification into strategies, concepts and models.
(Here it is as a PDF.)

There's things that are quite sophisticated present (hierarchical structuring, Van Hiele level 2 and level 3 reasoning) and very accessible things missing (motions, congruence and similarity). Even though they are not included, of course, you can still teach them; use those ideas to help students access the ideas that are required.

As I develop and revise activities for the course I'll be sure to share them. Again, if you have feedback about the landscape, shout it out!